1. Field of the Invention
The present invention relates to methods of detecting of amplitude values of electric quantities such as alternating voltage, alternating current or the like in electric systems, and more particularly to a detecting method where the frequency characteristics of a quantity to be detected are improved so as to obtain the amplitude value with little error.
2. Description of the Prior Art
FIG. 1 is a diagram explaining the principle of a prior art digital processing device for AC electric quantity measurement, disclosed in Japanese patent application No. 333434/1987, where sampling is performed every 90.degree. of alternating current and its amplitude value is estimated using three data samples. In FIG. 1, assuming that present sampling value 1 is made i (0), sampling value 2 preceding the present value by one period (T) is made i (T) and sampling value 3 preceding the present value by two periods (2T) is made i (2T), respective sampling values 1-3 are squared in square operation steps 6-8, and the result of only the square operation step 7 is doubled in a twice operation step 32.
Results obtained in the square operation steps 6 and 8 and the twice operation step 32 are added in adding operation step 14 so as to obtain the sum total. If the sum total is divided by two in a dividing operation step 33 and its square root is estimated in a square root operation step 16, its output F.sub.n is obtained at a terminal 17 and becomes the amplitude value of the alternating current.
Next, operation will be described. For convenience of explanation, the AC eletric quantity shall be alternating current, and its maximum value is made I, instantaneous value i is made i=I sin.theta., fundamental frequency is made f.sub.0, and sampling period is 1/4 of the period of the fundamental frequency f.sub.0 and made T. In order to distinguish data per sampling time, nT (n=0, 1, 2, . . . , and n=0 donates the present time) is used as a suffix, and i is expressed as i (0), i (T), i (2T), . . .
This is expressed by following formula (1). ##EQU1##
The sampling period T is fixed to 1/4 period with respect to the fundamental frequency f.sub.0 of the alternating current, i.e., the time interval corresponding to 90.degree. in electric angle. If the frequency is f, the sampling period T is expressed by following formula (2). ##EQU2##
For example, if frequency of the alternating current f=f.sub.0 =50 Hz, the sampling period becomes T=90.degree..
In general when the electric power system is operated at the rated frequency f.sub.0, formula (1) becomes F.sub.n =I and amplitude value operation of the current is possible and this is utilized, for example, in an AC overcurrent protective relay, a control device or the like. However, for a protective relay to detect faults in the electric power system and a control device for detecting electric quantities to control operating facilities, the frequency of the electric power system is often varied from f.sub.0, and the amplitude value must be estimated accurately even if the frequency is slightly shifted. In ordinary cases, the amplitude value measurement error must be reduced as much as possible to accommodate variation of the frequency of about .+-.5 %.
If the frequency becomes f=52.5 Hz (5% increase of 50 Hz ), the sampling period becomes T=94.5.degree. and substituting this in formula (1), F.sub.n becomes EQU F.sub.n =I{1-0.0062 cos (2.theta.-189.degree.)}.sup.1/2 ( 3)
in form that an oscillation waveform of twice the frequency is superposed with constant value. Since cos (2.theta.-189.degree.) can be varied in range of +1.0 to -1.0, formula (3) becomes EQU F.sub.n =0.997I to 1.003I (1)
thereby error of -0.3% to +0.3% is produced in comparison to the amplitude value measurement operating in the case of the rated frequency 50 Hz.
Since the electric quantity detecting method in the prior art is costituted by each operating step as above described and performs the amplitude value operation, a problem exists in that the amplitude value operation error is relatively large when the frequency varies about .+-.5%.